On the ratios of the individual latent roots to the trace of a Wishart matrix

Abstract

A simple relationship is given between the exact null distribution gm,n(J) of the J-th largest latent root of an m × m Wishart matrix on n degrees of freedom, and the distribution fm,n(J) of the ratio of this root to the trace of the matrix. Explicit expressions for certain fm,n(J) may thus be obtained from previous results for the corresponding gm,n(J).